1 research outputs found
Quasi-convexity of the asymptotic channel MSE in regularized semi blind estimation
In this paper, the quasi-convexity of a sum of quadratic fractions in the
form is demonstrated
where and are strictly positive scalars, when defined on the
positive real axis . It will be shown that this quasi-convexity
guarantees it has a unique local (and hence global) minimum.
Indeed, this problem arises when considering the optimization of the
weighting coefficient in regularized semi-blind channel identification problem,
and more generally, is of interest in other contexts where we combine two
different estimation criteria.
Note that V. Buchoux {\it et.al} have noticed by simulations that the
considered function has no local minima except its unique global minimum but
this is the first time this result, as well as the quasi-convexity of the
function is proved theoretically